X720

EVEN (- 3, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X720 lies on the line at infinity.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 30, 511 }: Central Line L(30, 511) { 6, 561 }: Central Line L(6, 561) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_721 = EVEN (- 3, 0) CIRCUMCIRCLE POINT (1.0101, 0.0860) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_720 = EVEN (- 3, 2) INFINITY POINT (0.0849, -0.1737) A B C X721 X30 X511 X6 X561 X720 (a, b, c) = (5, 6, 7) | AB = 1

X720 (EVEN (- 3, 2) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a ^{-4}(b^{2} + c^{2}) - a^{1}(b ^{-3} + c ^{-3})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines2 lines

{6, 561}, {30, 511}

▸ Functional Relations1 relation